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Attractors and neoattractors for 3D stochastic Navier-Stokes equations

Research output: Contribution to journalArticle

Author(s)

  • H.J. Keisler
  • N.J. Cutland

Department/unit(s)

Publication details

JournalStochastics and Dynamics
DatePublished - Dec 2005
Issue number4
Volume5
Number of pages46
Pages (from-to)487-533
Original languageEnglish

Abstract

In nonstandard analysis was used to construct a (standard) global attractor for the 3D stochastic Navier–Stokes equations with general multiplicative noise, living on a Loeb space, using Sell's approach. The attractor had somewhat ad hoc attracting and compactness properties. We strengthen this result by showing that the attractor has stronger properties making it a neo-attractor — a notion introduced here that arises naturally from the Keisler–Fajardo theory of neometric spaces. To set this result in context we first survey the use of Loeb space and nonstandard techniques in the study of attractors, with special emphasis on results obtained for the Navier–Stokes equations both deterministic and stochastic, showing that such methods are well-suited to this enterprise.

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